Under part-load conditions, a Francis turbine often suffers from very severe low-frequency and large-amplitude pressure fluctuation, which is caused by the unsteady motion of vortices (known as “vortex ropes”) in the draft tube. This paper first reports our numerical investigation of relevant complex flow phenomena in the entire draft tube, based on the Reynolds-averaged Navier–Stokes (RANS) equations. We then focus on the physical mechanisms underlying these complex and somewhat chaotic flow phenomena of the draft-tube flow under a part-load condition. The flow stability and robustness are our special concern, since they determine what kind of control methodology will be effective for eliminating or alleviating those adverse phenomena. Our main findings about the flow behavior in the three segments of the draft tube, i.e., the cone inlet, the elbow segment, and the outlet segment with three exits, are as follows. (1) In the cone segment, we reconfirmed a previous finding of our research group based on the turbine’s whole-flow RANS computation that the harmful vortex rope is an inevitable consequence of the global instability of the swirling flow. We further identified that this instability is caused crucially by the reversed axial flow at the inlet of the draft tube. (2) In the elbow segment, we found a reversed flow continued from the inlet cone, which evolves to slow and chaotic motion. There is also a fast forward stream driven by a localized favorable axial pressure gradient, which carries the whole mass flux downstream. The forward stream and reversed flow coexist side-by-side in the elbow, with a complex and unstable shear layer in between. (3) In the outlet segment with three exits, the forward stream always goes through a fixed exit, leaving the other two exits with a chaotic and low-speed fluid motion. Based on these findings, we propose a few control principles to suppress the reversed flow and to eliminate the harmful helical vortex ropes. Of the methods we tested numerically, a simple jet injection in the inlet is proven successful.
Design of Experiments Applied to Francis Turbine Draft Tube to Minimize Pressure Pulsations and Energy Losses in Off-Design Conditions
